Yvette Cooper interview: 'I just want to be the next Home Secretary'

With the polls showing that Ed Miliband's No 10 prospects are far from secure, Jane Merrick asks a member of his shadow Cabinet where her own ambitions lie

Yvette Cooper: I’m sure there will be a female Labour leader in future. Right now, let’s get Ed elected (Charlie Forgham-Bailey)

When Gordon Brown stood down as Labour leader after losing the 2010 election, Yvette Cooper wrote a detailed explanation of why she did not want to join the race to be his successor. With three children, the youngest then aged five, she said: "This isn't the right time for me" – but ended the article with a tantalising pay-off: "As for future leadership contests, who knows …"

Now, as we head into Labour's 2013 conference, Ed Miliband's Downing Street prospects look less than secure. We are nearly 18 months away from the general election, and his soft poll lead suggests that it is far from certain Labour can win outright. When Labour looks at who could replace him, the name of Yvette Cooper always comes up. Ed Balls, her husband, came third in the 2010 contest and surely could not stand again. For those who long for Labour to have a female leader, the shadow Home Secretary seems a sure bet.

Sitting in her second-floor office in the Commons before she decamps to the Brighton conference, the air in Westminster thick with questions over whether Miliband knew about Damian McBride's damaging smear campaigns, it is fair to ask whether she wants to be leader one day. But Cooper is blunt: "No. I want to be the Home Secretary." And that is that. No coy, 'there's no vacancy' or even that she has 'no ambition to be leader'. Just a flat, outright No.

When is the party going to get female leader? "I am sure there will be one in future … Right now, what we're trying to do is get Ed elected to No 10 and win the election."

Of course, she will be asked the leadership question again if Labour doesn't win in 2015. Voters in the wider world remain unconvinced over Miliband. Then there's the issue of McBride's memoirs.

Cooper shakes her head in disgust. "I started to read them, and to be honest I gave up. Yes, it was shocking and an unacceptable way to do politics, but it also felt like a kind of internal navel-gazing, which I think we've put behind us now."

She insists neither she nor her husband knew what McBride was up to. "I don't think either Ed or Ed knew the things that were in the papers or what was happening." This, she claims, is proven by how well the Eds get on together now.

"It's very sad where it had got to in the Blair/Brown relationship. You look back on it and you think, this actually didn't seem like it had anything to do with [her constituency] Pontefract and Castleford. And it certainly doesn't now; it feels even less relevant to the things that people are worried about."

Despite the former home secretary Jacqui Smith's characterisation of Labour policy as a "pregnant panda" – people wait a long time for something that may not be there – Labour unveiled a flurry of policies this conference weekend. Cooper, Labour's equalities spokeswoman as well as shadow Home Secretary, is pledging a new national commissioner for domestic and sexual violence, and is overseeing a policy review of maternity leave.

As a mother of three, Cooper knows all about problems when on maternity leave. She was the first minister in the British government to go on maternity leave, in 2001, with her second child. When she took leave for her third, in 2004, she felt civil servants cut her off. After talks with Harriet Harman and Patricia Hewitt, two of Labour's trailblazing women, new guidelines were set up in Whitehall. But when Jo Swinson, the pregnant Liberal Democrat employment minister, asked Cooper to share her experience, the Labour politician was aghast to find no one had heard of the guidance.

Labour has more support among women than men, but the party is vulnerable, particularly in its northern heartlands, on immigration. Ukip threatens the Conservatives in the South, but in the North the party is hard on the heels of Labour. How does Cooper think Labour can reassure these voters on immigration?

"We recognise the things we got wrong in government, particularly the transitional controls in Eastern Europe; [we were] too slow to bring in the points-based system … so the pace of migration was much higher than expected; it was too fast. That's why it's right to support controls that bring the level of migration down."

But the Home Office's vans urging illegal immigrants to go home were an "outrageous gimmick".

"People are feeling so stressed and pressured that they are looking around for things to make their voices heard. As a result of that pressure, what the Labour Party's got to do is recognise the pressures and respond to them with practical things we could do around the cost of living."

Talking to senior Lib Dems at their party conference in Glasgow, there was a strong feeling that Ed Balls could be the deal-breaker to a Lib-Lab pact in any coalition talks in 2015. When I put this to Cooper, she bristles – understandably, I guess, given I'm being rude about her husband.

"The Lib Dems have gone along with a lot of pretty nasty Tory policies. I think there's a lot of things we disagree with them on and that's what we'll be saying to the public."

Cooper is more amused when I ask if her husband makes her wince talking about pulled pork barbecues and crying at the Antiques Roadshow. "Yes," she says, laughing, before adding that Balls also weeps at The Sound of Music – particularly when Captain von Trapp finds the children singing "The Hills Are Alive" – the first time there has been music in the house since their mother died. Von Trapp (and, I imagine, the Shadow Chancellor) joins in with the harmonies. "He does well up, every time."